论文标题
部分可观测时空混沌系统的无模型预测
Delaunay-like Triangulation of Smooth Orientable Submanifolds by L1-Norm Minimization
论文作者
论文摘要
在本文中，我们研究了形状重建问题，当我们希望重建的形状是欧几里得空间的可定向的平滑D维次曼叶。假设我们具有近似亚体（例如Cech Complex或Cech Complex或Rips Complex）的简单复合物K，我们重新阐述了重新构成K中的Submanifold作为L1-norm最小化问题的问题，在该问题中，优化变量是K. K. K.的D-Chain是K。与在同伴论文中引入和研究的平坦Delaunay综合体相吻合。由于目标是加权的L1-词，并且约束是线性的，因此可以通过线性编程实现三角调节过程。
In this paper, we study the shape reconstruction problem, when the shape we wish to reconstruct is an orientable smooth d-dimensional submanifold of the Euclidean space. Assuming we have as input a simplicial complex K that approximates the submanifold (such as the Cech complex or the Rips complex), we recast the problem of reconstucting the submanifold from K as a L1-norm minimization problem in which the optimization variable is a d-chain of K. Providing that K satisfies certain reasonable conditions, we prove that the considered minimization problem has a unique solution which triangulates the submanifold and coincides with the flat Delaunay complex introduced and studied in a companion paper. Since the objective is a weighted L1-norm and the constraints are linear, the triangulation process can thus be implemented by linear programming.
